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Abstract
Detecting seismic events using a fiber-based CW laser interferometer attracts wide attention. To make the detection more effective, we analyze the system’s noise level by setting up two vibration detection systems. By changing the fiber length (0∼100 km) and laser noise level, respectively, we detect the minor phase change caused by a 160 µm-fiber-length vibration. Furthermore, we use three indicators, Power Spectral Density, Background Noise Level, and Signal-to-Noise Ratio to analyze the noise level of the whole system. The relation between the system’s background noise and corresponding detection result is carried out. This quantitative research can serve as a reference and help people to realize the most efficient vibration detection system.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays, due to the booming development of the internet and mobile services, optical fiber cables have been spread all over the world [1,2]. Beside data transmission, time-frequency synchronization in metrology related fields also relies on fiber network [3–9]. Furthermore, an emerging application using fiber network as sensors to explore environmental information has attracted wide attention in seismology [10,11], hydrogeology [12,13], traffic monitoring [14,15] and pipeline integrity threat detection [16–18] fields.
A mature fiber detection technology is distributed acoustic sensing technique (DAS), which mainly uses Rayleigh-Scattering of the injected laser pulse to extract vibration information along the fiber [19,20]. However, the detection length of DAS is limited by fiber attenuation and dispersion, and it can hardly be applied to long-distance fiber cable. In addition, the optical spatial resolution of DAS depends on the pulse width, which means DAS must balance between resolution and Signal-to-Noise Ratio (SNR) [21]. In recent years, a kind of CW laser interferometric detection has been demonstrated in seismic wave sensing [22]. It detects the phase fluctuation of a CW laser and is suitable for long commercial fiber links. However, the laser source in [22] is ultra-stable laser with Fabry-Pérot cavity [23], which is expensive, bulky and fragile [24]. This will limit its wide applications in the area of intercity vibration detection using urban fiber network. To investigate whether commercial laser module can undertake this detection task, noise level of the detection system (laser source and fiber link) should be evaluated and compared to the power level of target vibration signals.
In this paper, we use three indicators, Power Spectral Density (PSD), Background Noise Level (BNL) and SNR, to analyze the noise level of vibration detection system. Through changing fiber length and laser noise level, a quantitative analysis of the system’s background noise and its corresponding detection result has been carried out. This relation can serve as a reference of CW laser vibration detection system, for example, selecting the suitable laser (noise level) to realize a most effective and cost efficient fiber vibration detection.
2. Experimental setup
Figure 1(a) is the simplified diagram of the CW laser vibration detection system [25,26]. Heterodyne configuration can be realized with insertion of a frequency shifter ${\nu _{AOM}}$ in delay arm of the interferometer. ${\tau _\textrm{0}}$ is the time delay difference between two arms. When vibration occurs on the delay arm, corresponding phase change can be detected and recorded using phase measurement system. The basic diagram is unbalanced Mach-Zehnder interferometer, which uses a fiber link to realize the time delay difference ${\tau _\textrm{0}}$, thus we describe the fiber link as “unbalanced fiber link”. In practical application, one has to face the problem that the system background noise may overwhelm the target vibration. This is the reason why previous works focus on much higher perturbations like seismic waves and high-power vibrations. If we want to detect more kinds of vibration sources, a study should be carried out to make clear the noise level limitation of such a system.
Fig. 1. (a) Heterodyne interferometer, PD (Photodiode). (b) Experimental setup of vibration detection system, AOM (Acousto-Optical Modulator), FST (Fiber Stretcher), DAQ (Data Acquisition), Laser 1 (NKT Koheras BASIK Laser Module), Laser 2 (RIO Orion− Laser Module).
Consequently, as shown in Fig. 1(b), we set up two vibration detection systems to detect the same target vibration simultaneously. The components in vibration detection system 1 (System 1) are marked in blue, the components in vibration detection system 2 (System 2) are marked in green, and the common components are marked in black. In System 1, CW laser from Laser 1 splits into two beams. One beam on reference arm reaches the blue photodiode (PD) directly. The other beam on delay arm goes through the blue optical circulator and the fiber link, finally interferes with the former beam on PD. The principle of System 2 is similar to System 1. They can serve as the comparator and calibrator to each other. Laser 1 is a NKT Koheras BASIK module and Laser 2 is a RIO Orion module. Their linewidths are around 1000 Hz, while the linewidth of Laser 1 is a little narrower than Laser 2. They emit CW laser in opposite direction, their phase delay differences are acquired by Data Acquisition (DAQ) system with 100 kS/s sampling rate. Here, we use a fiber stretcher (FST) as vibration source to provide a controllable target vibration. It is a 1.5 Hz sine wave with 160 µm-fiber-length change (peak to peak). Apart from the target vibration, phase perturbations caused by laser source and fiber link are considered as the system background noise. Using an IQ demodulator, the beat-note detected by PD is compared with the reference signal. Thus, the in-phase (I) and quadrature (Q) components of phase delay difference can be acquired by DAQ system. Using the phase information, we can calculate its character in time and frequency domain [27]. In time domain, the detected phase changes caused by vibration are plotted in Fig. 2, where the linear trend has already been removed.
Fig. 2. Detected phase changes of target vibration. (a) ∼ (d) Phase changes detected by System 1, with unbalanced fiber length 0, 5, 50, and 100 km, respectively. (e) ∼ (h) Phase changes detected by System 2, with unbalanced fiber length 0, 5, 50, and 100 km, respectively.
As we can see, when the unbalanced fiber length is changed from 0 km to 100 km, both detection systems are available to detect the target vibration. It is noticeable that the level of background noise increases heavily along with fiber length. Besides, comparing with results of System 2, detected signals of System 1 have a smoother curve and higher SNR due to its narrower linewidth. All these phenomena qualitatively show that noise from laser source and fiber link deteriorates detection results, and the noise can be regarded as background noise of the detection system.
To quantitatively describe the background noise and detection result, we theoretically analyze the PSD of the detected phase information and investigate its changes in different experimental conditions.
3. Theoretical analysis
The laser signal in reference arm in Fig. 1(a) can be described as:
When there is no target vibration, the laser signal in delay arm can be described as:
The beat-note in PD is as follows:
Via the IQ demodulator and DAQ system, we can get the background phase information:
If we add a vibration on FST, the synthetic phase information will become $\; {\phi _{BG}}(t )+ {\phi _{SG}}(t )$, where ${\phi _{SG}}(t )$ is the phase changes caused by the target vibration signal.
The PSD of the background phase information $\; {\phi _{BG}}(t )$ and the synthetic phase information ${\phi _{BG}}(t )+ {\phi _{SG}}(t )$ can be calculated as [30]:
To simplify the analysis, the PSD of $\; {\phi _{BG}}(t )$ can be modelled by power laws [31], and the target vibration signal is considered to be a sine wave. We will get
where f is the offset frequency away from the center frequency ${\nu _0}$, k is the power density coefficient, ${\nu _{SG}}$ is the frequency of target vibration (1.5Hz in our case). Since the PSD of $\; {\phi _{BG}}(t )$ exists, its spectral density $\; S(f )$ existsWe can calculate the PSD of ${\phi _{BG}}(t )+ {\phi _{SG}}(t )$ as
Normally, people can assume that the target vibration can be detected as long as the background noise level doesn’t rise above the power level of vibration signal. While, taking fidelity into account, the level of background noise must be somehow lower than the power level of target signal. Detailed relation between the SNR and background noise level should be carried out.
4. Experimental results
Using the acquired raw data (without linear trend movement as operated in Fig. 2), Fig. 3 gives the calculated PSD of the background phase information ${\phi _{BG}}(t )$ and the synthetic phase information ${\phi _{BG}}(t )+ {\phi _{SG}}(t )$ when we add a vibration on FST (1.5 Hz sine wave with 160 µm-fiber-length change peak to peak).
Fig. 3. Power Spectral Density of phase information with different unbalanced fiber length. (a) PSD of ${\phi _{BG}}(t )$ detected by System 1. (b) PSD of ${\phi _{BG}}(t )+ {\phi _{SG}}(t )$ detected by System 1. (c) PSD of ${\phi _{BG}}(t )$ detected by System 2. (d) PSD of ${\phi _{BG}}(t )+ {\phi _{SG}}(t )$ detected by System 2.
Figure 3(a) and Fig. 3(b) are the PSD of ${\phi _{BG}}(t )$ and ${\phi _{BG}}(t )+ {\phi _{SG}}(t )$ detected by System 1, respectively. Figure 3(c) and Fig. 3(d) are the PSD of ${\phi _{BG}}(t )$ and ${\phi _{BG}}(t )+ {\phi _{SG}}(t )$ detected by System 2, respectively.
When there is no vibration, the power level of background phase ${\phi _{BG}}(t )$ increases dramatically as the fiber length increases. When we add a target vibration on the FST, a peak will appear at offset frequency around 1.5 Hz. The peak is similar to sinc function rather than delta function in Eq. (10), because the target vibration has a finite length in the experiment. The PSD of a finite length sine wave is sinc function, which also accords with our theoretical analysis. When unbalanced fiber length is 0 km, the PSD of ${\phi _{BG}}(t )$ detected by two systems (blue curve) is similar to each other, which means laser noise isn’t the main part in ${\phi _{BG}}(t )$ in 0 km-unbalance-fiber interferometer. In this case, the perturbations of fiber link and other electronic components play an important part. When unbalanced fiber length is 5, 50 and 100 km, the PSD of ${\phi _{BG}}(t )$ detected by two systems (orange curve, yellow curve and purple curve) differs from each other. The PSD of System 1 is lower than that of System 2 between 1 Hz and 100 Hz, which means Laser 1 has lower noise level than Laser 2 in this frequency range. The PSD of ${\phi _{BG}}(t )$ has a high slope below 1 Hz, which is caused by phase drift in time domain. In interferometer, environmental perturbations like temperature change usually induce slow phase drift. If linear trend of ${\phi _{BG}}(t )$ is removed, the PSD slope will decrease correspondingly.
Here, we use some indicators to quantitatively analyze the background noise level and the detection result. We can choose the indicator Background Noise Level BNL to character the level of system’s background noise ${\phi _{BG}}(t )$:
where HF and LF are the cut-off frequency of BNL pass-band. We set it to be 0.1–20 Hz in terms of the seismic wave bandwidth.The other indicator to describe detection result is Signal-to-Noise Ratio SNR, which is commonly used to represent signal’s quality:
where ${P_{SG}}$ and ${P_{BG}}$ are the power of target vibration signal and the background noise, respectively.The BNL and SNR of different unbalanced fiber length are listed in Table 1. Along with unbalanced fiber length increasing, the BNL increases and the SNR decreases, correspondingly.
Table 1. The BNL and SNR of detection systems with different unbalanced fiber lengths.
To investigate the relation between system BNL and detection SNR, further raising the fiber length doesn’t seem to be a smart method. On the basis of 100km-unbalance-fiber interferometer, we can use a white noise to deteriorate Laser 1 and increase the BNL of System 1. When we increase the white noise power step by step, the corresponding laser noise in System 1 will increase synchronously until we cannot detect the target vibration. As a calibration reference, we maintain the noise level of Laser 2, and System 2 can provide us timestamp of vibration signals. The BNL and SNR value of System 1 under different laser noise level are listed in Table 2.
Table 2. The BNL and SNR of detection system with different laser noise levels.
Using the SNR-BNL data of System 1 from Table 1 and Table 2, we plot the SNR-BNL relation in Fig. 4(a). The black points are obtained when we change fiber length (from Table 1), the blue points are obtained when we deteriorate laser noise (from Table 2). From the fitting curve (red curve), it can be seen that the SNR is inversely correlated with BNL. When the detection system’s BNL is low enough, the target vibration can be separated from background noise with high fidelity as the black curve in Fig. 4(b). When the BNL increases to 105 rad2, the detection result SNR dramatically drops to ∼10 dB. Further raising laser noise level, the BNL increases largely while the SNR decreases slowly. When BNL is around 3×105 rad2, the SNR is ∼ 2 dB and the waveform of target vibration is distorted significantly as the red curve in Fig. 4(b). Thus, the SNR-BNL relation can serve as a reference of CW laser vibration detection system. People have the choice to select SNR value in terms of their practical request and get the corresponding BNL. For example, a pattern recognition system [32] which requires a high fidelity needs a low-BNL system; while a detection system which just aims at vibration event recognition can relax the requirement on BNL of the interferometry system.
Fig. 4. (a) The SNR-BNL relation of System 1. Black points are from Table 1, blue points are from Table 2, red curve is the fitting curve of SNR-BNL relation of System1, magenta curve and green curve are the deduced SNR-BNL relation of vibration with different power. (b) Phase change caused by the target vibration signals. Black curve is detected by System 2 without deteriorating laser noise, red curve is detected by System 1 with deteriorating laser noise.
It should be noted that the SNR-BNL relation above is based on a vibration signal of certain power. In our case, it corresponds to 160 µm-fiber-length change (peak to peak) generated by a FST module. If the target vibration power changes, the quantitative relation between BNL and SNR will change as a result. It is reasonable to assume that for any vibration, there will be a corresponding SNR-BNL relation which is shown as the dotted curve (magenta curve and green curve) in Fig. 4(a). In practical application, to realize an effective CW laser vibration detection system, parameters such as target vibration power, required SNR and system’s BNL are of significant importance. After estimating the target vibration power and required SNR, the background noise BNL of detection system will be limited. As the BNL is mainly affected by laser noise and fiber length, different cases may be experienced. For example, if the laser source has been selected, the fiber length limitation can be made clear in terms of BNL. In another situation, if the fiber length is fixed, a most effective and cost efficient laser source may be chosen via the SNR-BNL relation analysis. In our case, since what we are interested in is the intercity network with fiber length within 100 km, we deteriorate our laser source step by step until reaching a poor detection result. In the process, we make clear the relation between laser noise and detection result. If we want to set up CW laser vibration detection systems on intercity network, the relation can be a reference to choose effective and cost efficient laser sources.
5. Conclusion
In conclusion, we set up two vibration detection systems to analyze the noise level of CW laser vibration detection system. The SNR-BNL relation between detection result and system’s background noise is carried out. It can serve as a reference for different applications of vibration detection. As long as the SNR-BNL relation is met, commercial laser module can also be used in vibration detection system. The quantitative analysis is useful in situation like vibration detection of intercity fiber network.
Funding
National Natural Science Foundation of China (61971259, 91836301); Ministry of Science and Technology of the People's Republic of China (2016YFA0302102).
Disclosures
The authors declare no conflicts of interest.
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